With the spread of coronavirus disease 2019 (COVID-19) and the unfolding of the emergency response against the ensuing epidemic, major hospitals across the world have successively issued emergency assistance announcements, calling for anti-epidemic facial masks, goggles, protective clothing and other emergency materials so as to support ongoing preventative measures1. Using the most comprehensive survey to date of nursing homes in the US during the COVID-19 pandemic, McGarry, Grabowski, and Barnett (2020) found that approximately one in five facilities faced shortages of PPE in early July, 2020. Although there was a slight decrease in the number facilities with shortages in PPE due to the higher availability of gowns, overall PPE and staff shortages had not meaningfully improved by late May, 2020.
Prior to the crisis, there was an interdependence of trade and production for medical supplies, with advanced industrial countries like the United States and Germany specializing in the relatively high-tech medical devices sector, with low-cost production hubs such as China and Malaysia being the leading producers of less technologically sophisticated personal protective equipment (PPE) products such as face masks, surgical gloves, and medical gowns (Gereffi, 2020). However, on balance, the shortage of N95 masks in the U.S. during the COVID-19 pandemic seems more like a case of policy failure rather than market failure (Gereffi, 2020). A foreseeable shortage of supplies and an increasing flow of both suspected and real cases of COVID-19 contributed to the pressures and concerns of health professionals (Neto, Almeida, & Esmeraldo, 2020). The accurate prediction and scientific allocation of emergency materials is a powerful guarantee of epidemic prevention and control. Furthermore, delivering adequate healthcare in the setting of ongoing pandemics is challenging (Kato, Miyakuni, Inoue, & Yamaguchi, 2020). In view of this, it is of great significance to make effective allocation decisions based on the dynamic evolution of epidemics, as well as the concrete situation of the demand for emergency materials in affected areas.
Regarding the prediction of requested supplies for major emergencies, scholars mostly conduct research based on forecasting models, rules and algorithms, such as case-based reasoning (CBR) analysis (Zhu, Sun, & Jin, 2016). There are a variety of simple techniques for forecasting a time series based on a weighted average of past time-series, seasonal cycles and time trends (Emmanuel, Thomas, & Refik, 2014; Zhu, Wang, Regan, & Sun, 2020; Zhu, Zhang, & Sun, 2019). Among the aforementioned, the auto-regressive integrated moving average (ARIMA) method is the most effective and widely used approach in modeling the time series for predicting the demand of emergency resources (Box, Jenkins, & Reinsel, 1994; Sheu, 2010). Chang, Tseng, and Chen (2007) applied data processing in a geographic information system, with the network analysis functioning to estimate the possible locations of rescue demand points and the number of needed pieces of rescue equipment. Sheu (2010) used a multi-criteria decision making method to determine the priority of supplies, proposing a dynamic demand prediction and allocation model for emergency supplies based on incomplete information. Holguín-Veras and Jalle (2012) focused on the application of time series analysis, especially with regards to ARIMA analysis, wherein their study modeled immediate responses to Hurricane Katrina, with the requests of emergency supplies and their time patterns being numerically estimated. Through the use of the embedded tabu search heuristic algorithm, Balcik and Yanıkoğlu (2020) developed a practical method for realizing the assessment of route feasibility and the rapid assessment of post-disaster supplies.
As implied above, due to the differing research ideas of scholars working in the field of emergency management, the various methods applied to the demand prediction of emergency supplies are also somewhat controversial. In view of the fact that the demand for emergency supplies presents a certain time series trend as an emergency response unfolds, most studies primarily use time series analysis to focus on the linear autocorrelation of the time series in the forecasting process, directly predicting the supply demand in the future based on the initial time series data. Other scholars generally apply the commonly used case-based reasoning method in the field of artificial intelligence, combining it with support vector machine models and BP (backpropagation) neural network algorithms so as to indirectly calculate the total demand through the relationship between the number of survivors and the amount of supplies, subsequently calculating the demand for different stages.
Although the above studies have - albeit to some extent and within some specific situations - solved the issues of demand forecasting, distribution and allocation, they have ignored the regression of the nonlinear sample set and the features of data mining in the time series of forecasting demand. Moreover, there is room for further improvement in forecasting accuracy. In the day-to-day operation of emergency response, misdeployment often occurs due to deviations of estimates from the actual response. Here, the situational settings and condition assumptions do not conform to the actual rescue situation, with some models being too complex to be widely used in emergency response decision-making (Zhu et al., 2019).
In this paper, through the construction of a time series fluctuation periodic function, the nonlinear problem in low-dimensional space is converted into a linear problem in high-dimensional feature space via the use of the SVM (Support Vector Machine) kernel function. Combining the method of time series analysis and support vector machines, and taking into account the prediction accuracy and stability of the combined model, the ARIMA method is applied to predict the sequence residuals. The SVM regression model is then established to forecast the nonlinear section, maximizing the distance between the two types of samples in the feature space in order to find the global optimal solution, thereby providing technical support for the quantitative forecasting demand of donated face masks in major public health emergencies.
Time series analysis-support vector machine combination model
(1) Autoregressive Integrated Moving Average model (ARIMA)
A classic unary linear time series forecasting model, ARIMA was jointly proposed by Box and Jenkins in the 1970s, subsequently dubbed the Box-Jenkins model. The actual prediction process of ARIMA(p,d,q) includes various steps, such as smoothing analysis, a differencing process, model selection, parameter estimation, and hypothesis testing, amongst others. In the acronym, AR and MA respectively stand for autoregressive and moving average, with p, q, d respectively denoting the number of autoregressive terms, the number of moving average terms, and the amount of differencing required to transform the time series into a stationary series.
In an ARIMA model, the predicted value \({\text{y}}_{t}\) is expressed as a linear function between the value of the past t-1 time points and white noise (random error), including AR and MA. The formula is as follows:
$${\text{y}}_{t}={a}_{1}{y}_{t-1}+{a}_{2}{y}_{t-2}+\dots +{a}_{p}{y}_{t-p}+{v}_{t}-{b}_{1}{v}_{t-1}-{b}_{2}{v}_{t-2}-\dots -{b}_{q}{v}_{t-q}$$
1
(2) Combined ARIMA-SVM model
An important algorithm in the field of machine learning, the support vector machine (SVM) approach was formally proposed by Vapnik (1998). It is generally divided into three categories: linear separability, linear inseparability, and nonlinear analysis. The kernel function is the key factor of nonlinear mapping in the SVM regression model. By using the kernel function, time-consuming and complicated inner-product operations in high-dimensional space can be neatly avoided. Currently, the commonly used SVM kernel functions include linear kernel functions, radial basis functions (RBF), polynomial kernel functions, and multi-layer perception (MLP). Of these, the linear kernel function and polynomial kernel function have strong generalization abilities as global kernel functions, though their learning and nonlinear approximation abilities need further improvement.
In light of the aforementioned, this paper adopts a local kernel function RBF with strong nonlinear approximation ability and strong learning ability. The model maps the characteristics of the nonlinear sample set into the high-dimensional space in order to achieve a better classification effect, whilst also attempting to fundamentally solve the non-linear problem in the time series for emergency supplies.
The building of the forecasting model involves three steps. First, the ARIMA model estimates a prediction of the demand for emergency supplies \({L}_{t}\) and the residual sequence \({N}_{t}\). Second, the proposed combined ARIMA-SVM model is used to predict the initial model \({N}_{t}\) to obtain \({N}_{t}{\prime }\). Finally, the combined forecasting sequence \({Y}_{t}\) is obtained by the sum of \({N}_{t}{\prime }\) and \({L}_{t}\) so as to correct the initial prediction. The above learning process is primarily based on the residuals of multiple iterations, which can expand the application range of the ARIMA model in the field of forecasting research and obtain a hybrid forecasting model that conforms to the evolution pattern of changes in the demand of supplies. The specific steps are shown in Fig. 1.